Fig. 4

The radial profiles of the velocity perturbations V against \(r_\eta \) in the fluid layer of different model geometries obtained for the cases with a \(r_k=1\), b \(r_k=3\), c \(r_k=10\), d \(r_k=30\) and e \(r_k=100\). In each diagram, the vertical axis indicates the dimensionless height, while the horizontal axis indicates \(\log _{10}r_\eta \). Shown in color and thin solid contours are the amplitudes of radial velocity perturbations V normalized by their maxima \(V_\text {max}\) for given \(r_\eta \). For the color scale for the distribution of \(V/V_\text {max}\), see the scale bar at the bottom of the figure. The contour lines are drawn for \(0.1\le |V/V_\text {max}|\le 0.9\) with the interval of 0.1. The green lines indicate the heights which yield \(V=V_\text {max}\) for given \(r_\eta \). In some cases where regions of stable thermal stratification exist, we also show by thick gray lines the heights below which the thermal stratification is stable